In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th term.

In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th term.

Solution :

9th term is 32805 t9  = 32805 ar8  = 32805   -----(1)

6th term is 1215 t6  = 1215 ar5  = 1215  -----(2)

(2) / (1)  ==> ar5/ar8  = 1215/32805

1/r3  = 1/27

(1/r)3  = (1/3)3

r = 3

By applying the value of r in (2), we get

a(3)5  = 1215  

a  = 1215/35

a  = 5(35)/35

a = 5

12th term :

t12  =  ar11

t12   =  5(3)11